3 Human Models, Field Uniformity, and Frequency Domain
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7.2 Methods for Estimating the Induced Current Inside the Human Body
181
On the other hand, the standing human can be simulated better by an ellipsoid
rather than a spherical model: an elliptical cross section is more realistic than a circular cross section. There is also a simple formula to describe the induced current
density in elliptical cross section: J = 2πfBσ(b4 x2 + a4 y2 )1/2 (a2 + b2 )−1 , where a and
b are the semi-major and semi-minor axes on the x- and y-axes, respectively. This
formula also has been adopted by some guideline-setting bodies, such as the American Conference of Governmental Industrial Hygienists (ACGIH) and the Institute of
Electric and Electronic Engineers (IEEE): see ACGIH (1995) and IEEE (2002).
7.2.3 Numerical calculation of induced current
Recent development in computing ability has enabled large-volume numerical computation of induced currents using an anatomically accurate human body with ﬁner
resolution. Several calculation methods for estimating the induced current inside the
human body have been developed based on Maxwell equations.
7.2.3.1 Finite element method
The ﬁnite element method (FEM) is a standard method of numerical calculation used
in many scientiﬁc ﬁelds. The advantage of this method for calculation of induced
currents inside the human body is that the FEM is suitable for simulation of the
complex shape of the human body. At Electricite de France (EdF), the TRIFOU
code has been applied to a human model with simpliﬁed internal organs (Baraton
and Hutzler 1995). The code is a combination of FEM with the boundary element
method (BEM). The FEM is applied to the human body, and the BEM is applied to
the boundary between human model and surrounding air.
7.2.3.2 Impedance method
An impedance method is a computational procedure used to solve a circuit equation
for 3-D impedance meshes that represent the human body. Gandhi and his colleagues
(Gandhi and Chen 1992; Gandhi et al. 2001) at the University of Utah and Stuchly
and her colleagues at the University of Victoria used this method in the earlier stages
of their studies (Xi and Stuchly 1994ab), applying it to an anatomical human model
having a resolution of 3.6 millimeters.
7.2.3.3 Scalar-potential, ﬁnite-diﬀerence method
A scalar-potential, ﬁnite-diﬀerence (SPFD) method is a ﬁnite-diﬀerence method
where a scalar potential is an unknown parameter. A human body is modeled by
voxels, and node equations are solved. The outer magnetic ﬁeld is expressed as a
vector potential. With this approach, the amount of calculations required is relatively
small. The method is used in the studies conducted by Stuchly and her colleagues
(Dawson et al. 1997ab) and by Dimbylow (1998) at NRPB. In the NRPB study, calculation was conducted with minimum resolution of 2 mm.
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7 Induced Current as the Candidate Mechanism for Explanation of Biological Eﬀects
7.2.3.4 Finite-diﬀerence, time-domain method
A ﬁnite-diﬀerence, time-domain (FDTD) method is used for the frequencies of the
microwave region. In the ELF region, this method is disadvantageous because of the
large number of repetitions required in the calculation. Therefore, Furse and Gandhi
(1998) introduced a frequency-scaling technique. Here calculation of induced current
is performed at 10 MHz, and the results then are converted into that of power frequency, using the linear relationship between induced current and frequency. Also,
this approach can be applied to scenarios where both magnetic and electric ﬁelds
exist simultaneously. The same method was also applied by Gustrau et al. (1999).
They used 5 MHz as the scaling frequency.
7.2.3.5 Boundary element method
A BEM (boundary element method) is used by Bottauscio and Conti (1997) at IEN
(Istituto Elettrotecnico Nazionale, Italy) and CESI (Centro Elettrotecnico Sperimentale Italiano) for a simpliﬁed human model. The advantages of a BEM are less input
data and good accuracy, provided the internal medium is simple.
7.2.3.6 Calculation method for an electrostatic problem
Accurate calculation methods that were developed originally for electrostatic problems can be applied to the problem of ELF magnetic induction in the human body, because the fundamental equation (Laplace’s equation) to be solved is the same for both
problems, provided that the quasi-static approximation is valid. That is the condition
for which displacement current can be neglected, i.e. σ ωε where ω is angular frequency and is permittivity of human model. The charge-simulation method (CSM)
and surface-charge method (SCM) are used by Yamazaki et al. (2001) of the Central
Research Institute of Electric Power Industry (CRIEPI) in Japan. These methods also
are boundary-dividing methods, and they have the advantages over volume-dividing
methods like FEM or Impedance Method in the amount of input data.
In the CRIEPI study, a simple human model constructed with axis-symmetric objects representing several major organs was used (Fig. 7.1). The eﬀect of the organ
conductivity values assigned to each organ was investigated (Fig. 7.2), by comparing the amplitudes of the induced currents at respective organs. As expected, large
diﬀerences occur in the values of the induced current for each organ, depending on
the assumed conductivity of each organ. Example of induced ﬁeld in the horizontal
crosssection of the heart is shown in Fig. 7.3.
7.3 Human Models, Field Uniformity, and Frequency Domain
In this section, unsolved problems relating to estimation of induced current inside the
human body are discussed brieﬂy. The three main issues are (1) human model used
for induced current calculation, (2) exposure condition, and (3) frequency concerns.
7.3 Human Models, Field Uniformity, and Frequency Domain
183
Fig. 7.1. Human model used by CRIEPI. This is a simple human model constructed with
axis-symmetric objects representing ﬁve major organs (brain, heart, lung, liver, and intestine).
7.3.1 Human models
Human models used for numerical computation of induced current distribution
inside human bodies are classiﬁed into two categories. The ﬁrst is an
anatomically accurate human model based on an image obtained by magnetic
resonance imaging (MRI) and a medical atlas of an anatomy. An output
(http://www.nlm.nih.gov/research/visible/visible human.html) of the US Visible
Human Project is sometimes used; it can be segmented into a resolution of 2 – 5
millimeters for computation (see Fig. 5.9). In addition, Japanese male and female
realistic models with 2 mm resolution have been developed (see Fig. 9.2, Nagaoka
et al. 2004). The second type of human model is a simpliﬁed one composed of a
relatively simple shape of an outlook and internal organ (Yamazaki et al. 2001).
The conductivity value allocated to each tissue or organ is essential for accurate
induced current calculation, because the induced current density is proportional to
the conductivity of the tissue concerned. However, the published conductivity values for each tissue or organ diﬀer considerably, depending on the biological citation
184
7 Induced Current as the Candidate Mechanism for Explanation of Biological Eﬀects
Fig. 7.2. Example of induced ﬁeld distribution on the cross sections of four human models
perpendicular to side-to-side uniform magnetic ﬁeld. These models diﬀer in assigned electric
conductivities (homogeneous and inhomogeneous models A,B,C).
selected. Moreover, in some reports, the anisotropic character of conductivity is considered for muscle.
A comprehensive investigation of tissue conductivity measurements of biological tissues was conducted by Gabriel and co-workers (Gabriel 1996, Gabriel et al.
1996abc). The output of this important work has become the standard reference for
tissue conductivity values used in modeling eﬀorts. The use of a standard source
of tissue conductivity values reduces variability, based on choice of conductivity
values, among diﬀerent models. It remains to be determined whether improved measurements providing more accuracy and increased spatial speciﬁcity can be obtained.
7.3.2 Field uniformity
In the previously mentioned studies, magnetic ﬁelds were assumed to be uniform,
allowing for easier computation and for easy comparison of the results. In addition,
in protection guidelines such as ICNIRP’s, the reference levels of magnetic exposure
7.3 Human Models, Field Uniformity, and Frequency Domain
185
Fig. 7.3. Example of induced electric ﬁeld in the horizontal cross section at the center of the
heart when exposed to 1 µT, 50 Hz vertical magnetic ﬁeld. The length of the arrow in the legend indicates electric ﬁeld of 5 µV/m. The induced currents can be calculated by multiplying
conductivity at every position with the electric ﬁeld.
are derived by assuming the magnetic ﬁeld is uniform, because the coupling between
outer magnetic ﬁeld and inner induced current is maximum under this condition.
On the contrary, the real-world exposures to intense magnetic ﬁelds mainly occur
in the position very close to a ﬁeld source, such as (1) near a power line conductor,
in the case of a worker near a “live” line, or (2) near an electrical appliance. In
these situations, in general, the magnetic ﬁeld is highly non-uniform. With a nonuniform ﬁeld, the coupling between the ﬁeld and the human body is relatively weak,
compared to that occurring with a uniform ﬁeld.
There are several reports, in the ELF range, that take into account non-uniformity
when performing their calculations. Some reports dealt with power lines (Baraton
and Hutzler 1995; Stuchly et al. 1996; Dawson et al. 1999abc), and others describe
electrical appliances, such as a hair dryer (Baraton and Hutzler 1995; Cheng et al.
1995; Kaune et al. 1997; Tofani et al. 1995ab). Considerable work remains to be
done in the description of real-world exposure situations and in numerical modeling
of the induced currents and ﬁelds occurring in models of the human body under these
situations.
186
7 Induced Current as the Candidate Mechanism for Explanation of Biological Eﬀects
7.3.3 Expansion of frequency range studied
Resent development of appliances using magnetic ﬁeld with a frequency higher than
that of the 50 or 60 Hz power system has raised a new interest in health eﬀects. Induction heating (IH) cookers are one of the newer appliances that utilize a higher
frequency, typically 20 kHz to 100 kHz, for heating of ferromagnetic pans. Another
concern is electric article surveillance (EAS) systems installed at the entry of buildings, such as grocery stores and libraries. These devices also use these ranges of frequency. These frequency ranges are sometimes called “intermediate frequency (IF)”
mainly in the European organizations (COST 1998; Matthes et al. 1999).
Because higher frequency ﬁelds induce higher induced currents inside the human
body, with the increase proportional to the frequency, existing protection guidelines
use more strict regulation of ﬁeld levels for higher frequency ranges. For example,
in the ICNIRP (1998) guideline, the reference level of magnetic exposure for the
public is 0.1 mT at 50 Hz. However, the permissible exposure is reduced greatly, to
0.00625 mT, at frequencies of a few tens of kHz. So far, only a few reports have
been published that focus on currents induced in the human body by magnetic ﬁelds
in this frequency range (Kaune et al. 1997; Gustrau et al. 1999; Gandhi and Kang
2001; Yamazaki et al. 2004).
7.4 Challenges to Interpretation of Biological Outcomes
One of the aims of estimation of the induced current occurring inside biological
object is to contribute to interpretation of the outcomes of biological experiments
with animals or cells. Stuchly and her co-workers have analyzed induced currents
in cell culture dishes considering cell membranes and gap junctions (Stuchly and
Xi 1994; Fear and Stuchly 1998ab). These eﬀorts contribute to clarifying the microscopic dosimetry of induced current in the experimental conditions used in cell exposure. Biological investigators are coming to understand that the exposure conditions
applied to their cells are not uniform: cells at the center of a culture dish can be at
relatively low ﬁeld exposure conditions while cells at the periphery of a dish, or near the
liquid interface with dish or with air, can be at relatively high ﬁeld exposure conditions.
Another concern is that the biological eﬀect caused by magnetic ﬁeld can be dependent on polarization of the ﬁeld (Kato et al. 1993). In this experiment, a circularly
polarized ﬁeld caused the biological eﬀect, suppression of melatonin, while linearly
polarized ﬁelds, either horizontal or vertical, did not (with the ﬁeld intensities examined). Furthermore, elliptically polarized ﬁelds of various degrees of circularity
produced intermediate eﬀects. The magnetic ﬁeld near an ordinary overhead transmission line is elliptically or circularly polarized. Thus, consideration of polarity
might clarify the literature on biological eﬀects of power-frequency magnetic ﬁelds.
There are some reports dealing with the induced currents produced by circularly
polarized currents (Misakian 1991, 1997; Yamazaki et al. 1996; Wake et al. 2000). It
should be noted that circular polarization of outer magnetic ﬁeld does not necessarily
mean circular polarization of induced current inside a biological object: the polarity
of the induced current can depend on the location within the organism.
7.5 Inter-laboratory Comparison Studies
187
2
Normarized Induced Current Density (µA/m )
(Magnetic Field: 1µT, 50Hz)
+%0+42
Yamazaki et al. 2001
Gustrau et al., 1999
Baraton et al., 1995
Bottauscio et al., 1997
Dimbylow, 1998
Gandhi et al., 1992
Dawson et al., 1997a,b
Xi and Stuchly, 1994b
Xi and Stucly, 1994a
+PJQOQIGPQWU
#XGTCIG
+PJQOQIGPQWU
/CZKOWO
*QOQIGPQWU
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Fig. 7.4. Comparison of estimated current density inside the human body when exposed to
uniform magnetic ﬁeld of 1 µT, 50 Hz. Among the nine studies examined, values varied by
almost two decades, and some exceed the ICNIRP standard.
7.5 Inter-laboratory Comparison Studies
In general, the result of numerical calculation must be veriﬁed by comparing it with
analytical or experimental values. The diﬃculty in the present problem is the inability to
verify results with in situ measurements. (Very little data will be available from electrodes
placed in human bodies under controlled exposure conditions.) Because of this limitation, many guideline-setting bodies have not adopted the recent, highly advanced
numerical calculation as their rationale for deriving limiting magnetic ﬁeld values.
Some eﬀorts have been conducted to compare the results of numerical calculation among diﬀerent research group (Stuchly and Dawson 2000; Stuchly and Gandhi
2000; Caputa et al. 2002). The comparisons showed good agreement, provided that
similar anatomical models and conductivity values were used. However, another effort used data from nine reports and showed large variation in induced current results
among the several studies. To allow comparison, the induced current values from
each study were converted to a standard intensity of the outer uniform magnetic ﬁeld
(Fig. 7.4).
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7 Induced Current as the Candidate Mechanism for Explanation of Biological Eﬀects
7.6 Summary
For a variety of reasons, induced current has long been considered to be the most
important measure of dose when dealing with biological eﬀects of applied or induced currents and ﬁelds. Electrostimulation has a long history in biology, dating
back to the work of Galvani and Volta in the early 19th century. Furthermore, the basic mathematical tools for describing ﬁelds and currents were developed in the 18th
century, especially by Faraday, Laplace, and Maxwell. Two centuries of biomedical
research have supported the view that current density is a prime independent variable
in bioelectromagnetics.
Given the importance of current as a basic mechanism, it has been the key component of eﬀorts to set safety standards to protect the public against any possible
adverse health eﬀects from environmental exposures to electric and magnetic ﬁelds.
Thus, a variety of computational models have been developed in recent years to
compute the induced current produced in the body by an external electric or magnetic ﬁeld. Furthermore, the development of anatomically correct images of the human body, coupled with assignment of accurate conductivity values to all tissues
and organs, has moved the discipline from simplistic, general, back-of-the envelope
computations to what are assumed to be highly accurate and precise computational
models. The tools now available handle anatomic detail down to voxels of about 2
mm per side.
It now is relatively straight-forward to implement commercially available or
investigator-developed codes on personal computers and minicomputers. Available
approaches now include (1) ﬁnite-element methods, (2) impedance methods, (3)
scalar-potential, ﬁnite-diﬀerence methods, (4) ﬁnite-diﬀerence, time-domain methods, (5) boundary element methods, and (6) electrostatic-based computations. Using
a basic standard of 10 mA/m2 as a safety threshold for the current induced in the
human body by an external ﬁeld, one can compute the induced current in all of the
various tissues or organs in the body and therefore determine if a given external ﬁeld
is likely to be safe or not.
Despite dramatic progress in the last few decades, important challenges remain.
Validation is a key issue with any computational model. Direct measurement of induced current is diﬃcult, and acquisition of additional good empirical data under a
variety of exposure conditions would be very helpful. Additionally, a 2 mm voxel
is biologically large (or even huge) for some targets; thus, ﬁner resolution might be
very useful. Comparison of the results from various models is just beginning: sometimes agreement is good, which is encouraging. However, sometimes agreement is
not so good, which is discouraging. It is important to understand how models agree
and disagree, and it also is important to understand the causes for similarities and
diﬀerences in results from various models.
Standards would be improved by inclusion of such real-world factors as ﬁeld inhomogeneity and polarity. Also, investigations need to be conducted over a wider
variety of frequencies. Because of the commercial importance of ELF power and
microwaves, these two regions have been studied more extensively than the intermediate frequencies between these extremes. As new technologies operating at diﬀerent
7.7 References
189
frequencies are developed and applied, the need for safety information continues to
develop.
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